Question

Решите пожалуйста : 2cos^3 x+cos(x-π) =0

Answer 1

$\displaystyle 2cos^3x+cos(x- \pi )=0\\\\2cos^3x+cos(-( \pi -x))=0\\\\2cos^3x+cos( \pi -x)=0\\\\2cos^3x-cosx=0\\\\cosx(2cos^2x-1)=0\\\\cosx=0; 2cos^2x-1=0$

$\displaystyle cosx=0\\\\x= \frac{ \pi }{2}+ \pi n; n\in Z$

$\displaystyle 2cos^2x=1\\\\cos^2x= \frac{1}{2}\\\\cosx=\pm \frac{1}{ \sqrt{2}}\\\\x=\pm \frac{ \pi }{4}+ \pi n; n\in Z$